Hybrid integrated circuit/microfluidic chips harness the nano-scale feature size, the programmability, and the GHz clock rates of modern semiconductor technology and combine them with the biocompatibility of microfluidics. Utilizing this approach, chips have been developed for the programmable dielectric and magnetic control of cells, detection of sparse soluble biomarkers, and the sensing of rare. While these chips have performed well in laboratory settings, a major hurdle to their further development is the inherent size mismatch between integrated circuits (“ICs”) (˜mm) and microfluidic chips (˜cm). Millimeter-sized ICs can be built with great functionality, primarily because of the nanoscale-features of modern ICs, which allow for enormously dense circuitry. Increasing the area of an IC to match the size of the microfluidic chip (˜100× increase in area), as has often been done in previous studies leads to a waste of valuable space on the IC, greatly increasing fabrication cost (>100×).